Question

Question: Hello all,I am working on a transient stability analysis project of DFIG and I am trying to use direct method. However, all the DFIG models I have come across all the dynamic equations expressed in the dq-axis. I have being trying without success to change to a line/phase voltage expression by simply applying the inverse transformation matrix. The problem I have is with the angles. Example I know Vds=(Vms)Sinwst and Vdr=(Vmr)sinwrt, but I don't know exactly what wst will be if i want to express it as a steady state value, because in synchronous machines the resulting steady state value becomes Vds=Vms(-Sin(delta)). I don't know if I have been very clear but I just want an equation for Vds, Vdr, Vqs and Vqr which are not time dependent and are interms of Vms and a trigonometric function of an angle.Thank you

Answer 1

Inverse Park Transformation

To transform the dq-axis variables to the line/phase voltage expressions, we can use the inverse Park transformation matrix:

T^{-1} = [cos(θ)  -sin(θ)  0][sin(θ)   cos(θ)  0][0         0       1]

where θ is the angle between the d-axis and the a-axis.

Steady-State Values

Assuming balanced three-phase conditions, the steady-state line/phase voltages can be expressed as:

Vds = Vms  sin(θ)Vdr = Vms  cos(θ)Vqs = 0Vqr = 0

Steady-State Angle

For a DFIG operating at steady state, the angle θ can be calculated from the machine speed (ω) and the synchronous frequency (ωs) as:

θ = arctan(ω/ωs)

This angle represents the phase displacement between the stator flux and the rotating magnetic field of the rotor.

Equations for Steady-State Line/Phase Voltages

Substituting the steady-state angle into the inverse Park transformation equations, we get:

Vds = Vms  sin(arctan(ω/ωs))Vdr = Vms  cos(arctan(ω/ωs))Vqs = 0Vqr = 0

These equations provide the steady-state line/phase voltage expressions in terms of the stator voltage (Vms) and the phase angle between the stator flux and the rotor field. Flag for review

Answer 2

Inverse Park Transformation

To transform the dq-axis variables to the line/phase voltage expressions, we can use the inverse Park transformation matrix:

Topic: DFIG-Stator and Rotor Voltages